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Physica Scripta

Peak doubling in spontaneous parametric down-conversion coincidence spectra with a short-pulse pump*

Mikhail Vladimirovich Fedorov, J. M. Mikhailova, P. A. Volkov

Published Apr 20, 2012• 1 citation
Publisher

Abstract

In this paper, we describe the double-peak structure of the coincidence spectrum of biphoton states in the process of spontaneous parametric down-conversion with a pump having the form of short pulses. The effect is shown to arise from the obligatory symmetry of biphoton wave functions that describe the states of two bosons obeying the Bose–Einstein statistics. Parameters of the peaks are found and the conditions under which the effect can be experimentally observed are determined

DOI
10.1088/0031-8949/85/05/058105

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In this paper, we describe the double-peak structure of the coincidence spectrum of biphoton states in the process of spontaneous parametric down-conversion with a pump having the form of short pulses. The effect is shown to arise from the obligatory symmetry of biphoton wave functions that describe the states of two bosons obeying the Bose–Einstein statistics. Parameters of the peaks are found and the conditions under which the effect can be experimentally observed are determined
The requirement for symmetry of the biphoton wave function results in a double-peak structure of the coincidence spectra of spontaneous parametric down-conversion (SPDC) [Fedorov, Mikhailova, and Volkov, Phys. Scr. 85, 058105 (2012)]. In this work we report the experimental observation of this effect by carefully tailoring parameters of the SPDC crystal, the ultrafast pump laser, and the measurement setup. The results are shown to be relevant to quantum state engineering of ultrafast polarization or frequency-entangled mixed states.
We investigate spectral and temporal features and entanglement of biphoton wave packets formed in spontaneous parametric down-conversion with a pulsed laser pump. The degree of entanglement is characterized by the experimentally measurable parameter RRR defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration $\ensuremath{\tau}$. The function $R(\ensuremath{\tau})$ is shown to have a minimum and even in the minimum, at rather natural conditions, the degree of entanglement is found to be very high (Rmin=73)({R}_{\mathrm{min}}=73)(Rmin​=73). The Schmidt number KKK is found analytically for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of RRR and KKK are found to be identical and numerical coefficients are found to be rather close. Two-time temporal wave function of a biphoton state is investigated in detail, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter Rt{R}_{t}Rt​ (defined as the ratio of durations of the single-particle and coincidence signals) is shown to be very close to the Schmidt number KKK.
Spectral and temporal coincidence and single-particle photon wave packets are described and their widths and durations are found. The degree of entanglement is characterized by the experimentally measurable parameter R defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration. This function is shown to have a minimum and even in the minimum, at rather natural conditions, the parameter R is found to be very high (R=73>>1). The Schmidt number K is found for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of R and K are found to be identical and numerical difference between them is shown to be not exceeding 20%. Two-time temporal wave function of a biphoton state is investigated in details, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter R is defined as the ratio of durations of the single-particle and coincidence signals, and the defined in such a way parameter R is shown to be very close to the Schmidt number K.
We report on experimental measurements of coincidence and single particle spectral shapes of biphoton signals when frequency entangled states are generated by SPDC crystals pumped by short pulses.It is shown evidence for biphoton coincidence spectrum narrower and single-particle one wider than the pump spectrum, with a large contrast between coincidence and singles distributions.The investigation of biphoton correlations has been performed by fixing one monochromator at the maximal transmission wavelength on down-converted signal gate and scanning the one placed in the idler branch in order to observe the spectral distribution of single counts and coincidences.The degree of entanglement is evaluated by the ratio of the FWHM of single particle and coincidence distributions: the greater the ratio, the greater is the entanglement.The degree of entanglement in frequency variables can be very high: it increases linearly with the length of the crystal, and decreases with the growing pump pulse.